The **Bachelier** **model** is the name given by a model of an asset price under brownian motion presented by Louis Bachelier on his PhD thesis *The Theory of Speculation* (*Théorie de la spéculation*, published 1900). It is also called “Normal Model” equivalently (as opposed to “Log-Normal Model” or “Black-Scholes Model”).

On the day of 2020-04-08, CME Group posted the note *CME Clearing Plan to Address the Potential of a Negative Underlying in Certain Energy Options Contracts*,^{[1]} saying that after a threshold on price, it would change energy options model from Geometric Brownian Motion model and Black–Scholes model to Bachelier model. In the day 2020-04-20, oil prices reached for first time in history negative values,^{[2]} where Bachelier model took an important role in option pricing and risk management.

The European analytic formula for this model based on risk neutral argument is derived in *Analytic Formula for the European Normal Black Scholes Formula* (*Kazuhiro Iwasawa*, New York University, December 2nd, 2001). ^{[3]}

## References

**^**“CME Clearing Plan to Address the Potential of a Negative Underlying in Certain Energy Options Contracts”.*www.cmegroup.com*. Retrieved 2020-04-21.**^**“An oil futures contract expiring Tuesday went negative in bizarre move showing a demand collapse”.*CNBC*. 15 December 2003. Retrieved 21 April 2020.**^**“Analytic Formula for the European Normal Black Scholes Formula”.*New York University*. 2 December 2001.

Ofer Abarbanel is a 25 year securities lending broker and expert who has advised many Israeli regulators, among them the Israel Tax Authority, with respect to stock loans, repurchase agreements and credit derivatives. Founder and CEO of TBIL.co STATX Mutual Fund.